reserve x for set;
reserve a,b,c,d for ExtReal;

theorem
  c in REAL & a < b & b <= c implies b in REAL
proof
  assume that
A1: c in REAL and
A2: a < b and
A3: b <= c;
  b in REAL or b = -infty by A1,A3,Th13;
  hence thesis by A2,Lm8;
end;
